Y is a ternary relation between them, i.e.,YCUxTXR, called assign ments and < is a user-specific subtag/supertag-relation, i. e, <CUX(TxT)\(t, t) t∈T}) The personomy Pu of a given user u E U is the restriction of F to u, P:=(T,Rn,l,xu) with I:={(t,r)∈T×R|(u,t,r)∈Y},Tn:=丌1(Ix) Ru:=丌2(lu), and <u:={(t1,t2)∈T×T(u,t,t2)∈} Users are typically described by their user ID, and tags may be arbitrary strings. What is considered as a resource depends on the type of system. In delicio us. for instance. the resources are URLs. and in Flickr. the resources are pictures. In our BibSonomy system, we have two types of resources, book marks and BIBTEXentries. From an implementation point of view, resources are internally represented by some ID In this paper, we do not make use of the subtag/ supertag relation for sake of simplicity. I.e., <=0, and we will simply note a folksonomy as a quadruple F: =(U,T, R, Y). This structure is known in Formal Concept Analysis(wille (1982), Ganter and Wille(1999)) as a triadic contert(Lehmann and Wille (1995), Stumme(2005)). An equivalent view on folksonomy data is that of a ripartite (undirected) hypergraph G=(V, E), where V= UUTUR is the set of nodes, and E= u, t, rl(u,t, r)EY is the set of hyperedges 2.3 Del.ico. us- A Folksonomy-Based Social Bookmark System In order to evaluate our folksonomy mining approach, we have analyzed the popular social bookmarking sytem del icio us. Delicio us is a server-based sys- tem with a simple-to-use interface that allows users to organize and share book- marks on the internet. It is able to store in addition to the url a description, a note, and tags(i. e, arbitrary labels). We chose delicio. us rather than our own system, Bibsonomy, as the latter is going online only after the time of writing of this article. For our experiments, we collected from the del. ico. us system U= 75, 242 users, T= 533, 191 tags and R=3, 158, 297 resources, related by in total Y= 17, 362, 212 triples 3 Association Rule Mining We assume here that the reader is familiar with the basics of association rule mining introduced by Agrawal et al. (1993). As the work presented in this pa- per is on the conceptual rather than on the computational level, we refrain in particular from describing the vast area of developing efficient algorithms Many of the existing algorithms can be found at the Frequent Itemset Min- ing Implementations Repository. Instead, we just recall the definition of the association rule mining problem, which was initially stated by Agrawal et al. (1993), in order to clarify the notations used in the following. We will not use http://fimi.cs.helsinkifi/ 4• Y is a ternary relation between them, i. e., Y ⊆ U × T × R, called assign￾ments, and • ≺ is a user-specific subtag/supertag-relation, i. e., ≺⊆ U ×((T ×T )\ {(t, t) | t ∈ T }). The personomy Pu of a given user u ∈ U is the restriction of F to u, i. e., Pu := (Tu, Ru, Iu, ≺u) with Iu := {(t, r) ∈ T × R | (u, t, r) ∈ Y }, Tu := π1(Iu), Ru := π2(Iu), and ≺u:= {(t1, t2) ∈ T × T | (u, t1, t2) ∈≺}. Users are typically described by their user ID, and tags may be arbitrary strings. What is considered as a resource depends on the type of system. In del.icio.us, for instance, the resources are URLs, and in Flickr, the resources are pictures. In our BibSonomy system, we have two types of resources, book￾marks and BibTEXentries. From an implementation point of view, resources are internally represented by some ID. In this paper, we do not make use of the subtag/supertag relation for sake of simplicity. I. e., ≺ = ∅, and we will simply note a folksonomy as a quadruple F := (U, T, R, Y ). This structure is known in Formal Concept Analysis (Wille (1982), Ganter and Wille (1999)) as a triadic context (Lehmann and Wille (1995), Stumme (2005)). An equivalent view on folksonomy data is that of a tripartite (undirected) hypergraph G = (V, E), where V = U∪˙ T∪˙ R is the set of nodes, and E = {{u, t, r} | (u, t, r) ∈ Y } is the set of hyperedges. 2.3 Del.ico.us — A Folksonomy-Based Social Bookmark System In order to evaluate our folksonomy mining approach, we have analyzed the popular social bookmarking sytem del.icio.us. Del.icio.us is a server-based sys￾tem with a simple-to-use interface that allows users to organize and share book￾marks on the internet. It is able to store in addition to the URL a description, a note, and tags (i. e., arbitrary labels). We chose del.icio.us rather than our own system, Bibsonomy, as the latter is going online only after the time of writing of this article. For our experiments, we collected from the del.ico.us system |U| = 75, 242 users, |T | = 533, 191 tags and |R| = 3, 158, 297 resources, related by in total |Y | = 17, 362, 212 triples. 3 Association Rule Mining We assume here, that the reader is familiar with the basics of association rule mining introduced by Agrawal et al. (1993). As the work presented in this pa￾per is on the conceptual rather than on the computational level, we refrain in particular from describing the vast area of developing efficient algorithms. Many of the existing algorithms can be found at the Frequent Itemset Min￾ing Implementations Repository.13 Instead, we just recall the definition of the association rule mining problem, which was initially stated by Agrawal et al. (1993), in order to clarify the notations used in the following. We will not use 13 http://fimi.cs.helsinki.fi/ 4